The monetary multiplier shows the multiple by which the money stock can expand given an initial infusion of fresh funds into the banking system.
A central bank, such as the Federal Reserve System, can infuse additional funds into commercial banks by purchasing government bonds owned by commercial banks or commercial bank customers. The central bank can also loan funds to commercial banks, but purchasing bonds has a more permanent impact.
A customer of a commercial bank sells a bond to the Federal Reserve System, taking the proceeds of the sale and depositing it in an account at the commercial bank. Under a fractional reserve system of banking, the commercial bank has to hold only a fraction of the new deposit, say 20 percent if the legal reserve ratio is 20 percent, and the remainder the commercial bank can lend to a borrowing customer. Whatever amount is loaned out is likely to be deposited in either the bank making the loan, or more likely, in another bank. The bank that receives this second deposit originating from the bank loan only has to keep a fraction of the new deposit, and can lend the remainder. Therefore a second loan will be made.
The customer that first sold a bond to the Federal Reserve System still has the proceeds of that sale in the form of a bank deposit, and two subsequent bank deposits have been created, causing a magnified expansion of the money supply, the bulk of which is bank deposits. The expansionary process will continue, as the proceeds of a second loan will, in all probability, land in a bank deposit, giving another bank a new deposit from which it can make a loan. Each bank that receives a new deposit must hold a fraction of the new deposits as reserves, and may lend the remainder.
Because each subsequent new deposit is smaller than the previous new deposit, the cumulative expansion of new deposits slows to a halt. The monetary multiplier shows how far bank deposits could theoretically expand under ideal conditions. If the monetary multiplier is five, then an initial infusion of $1,000 of fresh funds into commercial banks could lead to a maximum expansion of bank deposits of $5,000.
The simplest monetary multiplier is calculated by taking the reciprocal of the legal reserve ratio. A legal reserve ratio of 20 percent produces a monetary multiplier of five. This simplest multiplier ignores the possibility that banks may purposely maintain a reserve ratio above the legal reserve ratio, or that some funds loaned out by a bank may leak into circulation, never to be deposited in another bank. In practice the actual monetary multiplier will be less than the theoretical monetary multiplier based only on the legal reserve ratio.
More complicated multipliers incorporate a currency to deposit ratio to adjust for the leakage of cash into circulation.
The funds that the Federal Reserve System injects into commercial banks is sometimes called high-powered money, because a series of commercial banks making loans will multiply that initial injection of funds into a much larger money stock increase. The monetary multiplier also shows that the money supply is not entirely in the hands of the Federal Reserve System, but expands and contracts with the eagerness of commercial banks to make loans, giving the commercial banks as much influence on the money supply as the printing presses at the Bureau of Engraving.